Secretary of State Mike Pompeo made his first trip to Russia on Tuesday to meet with Foreign Minister Sergey Lavrov and President Vladimir V. Putin. Mr. Pompeo hopes to discuss arms control, Iran and Venezuela.CreditCreditPool photo by Pavel Golovkin

Secretary of State Mike Pompeo made his first diplomatic trip to Russia on Tuesday to meet with his counterpart, Foreign Minister Sergey Lavrov, and President Vladimir V. Putin.

The three have a great deal of territory to cover, from many bubbling international conflicts — where Washington and Moscow have often found themselves on opposite sides — to a potential new arms treaty. It is the highest level meeting between American and Russian officials since President Trump met with Mr. Putin in Finland last July.

As the meeting with Mr. Lavrov began, Mr. Pompeo said the discussions were intended to improve ties between the two nations, to “stabilize the relationship,” and to find issues where the two powers had “overlapping interests.”

Here are the issues that are likely to be at the forefront of discussions at the meeting in the Black Sea resort city of Sochi.

Arms control

Ahead of Mr. Pompeo’s trip, a senior State Department official told reporters that an arms control agreement would be at the top of the agenda.

The treaty — signed in 1987 by President Ronald Reagan and Soviet leader Mikhail S. Gorbachev and seen as one of the most important nuclear agreements in history — limited the development and deployment of intermediate-range missiles designed to deliver nuclear warheads. It will come to an end this summer if no action is taken by either side. During the Obama administration, the United States concluded that Russia had been in violation of the treaty since at least 2014, though Moscow disputes that.

Analysts have long highlighted the limitations of the treaty, which did not take into account the development of the same weapons systems by other nations, including China. Earlier this month, President Trump said that in a phone call with Mr. Putin he had discussed the potential for a new, three-way deal on nuclear arms that would include China.

Renewed tensions with Iran

Since President Trump last year announced America’s withdrawal from the Iran nuclear deal, his administration has slowly reinstated punishing sanctions on Tehran. In recent weeks, Iran signaled it would reduce compliance with the restrictions imposed by the agreement unless the European parties to the deal provide Tehran with promised economic benefits. That seems unlikely, in that European companies refuse to do business with Iran for fear of the American sanctions.

Since then, tensions with Iran have dominated Mr. Pompeo’s agenda, and the issue is certain to be discussed again on Tuesday. Earlier this month, the United States sent an aircraft carrier strike group and B-52 bombers to the Persian Gulf, citing Iranian threats.

Then the secretary of state canceled a trip to Germany and instead traveled to Baghdad to meet with Iraqi officials, to discuss what he called the increased dangers from Iran’s forces and allies. He also went to Brussels to discuss concerns over Iran with European leaders.

Russia and Iran are strategic allies in Syria, and recently announced they would hold joint naval exercises in the Persian Gulf this year. Mr. Lavrov, in a news conference this month with Foreign Minister Mohammad Javad Zarif of Iran, denounced the “unacceptable situation” created by the “irresponsible behavior of the United States” in regard to the sanctions.

On Monday, a day before his meeting with Mr. Pompeo, Mr. Lavrov reiterated Russia’s stance, calling the American sanctions on Iran “illegitimate” during a news conference in Sochi. He said that he planned to have a “candid” conversation with Mr. Pompeo about the issue and encouraged the European nations that remain part of the agreement to aid Iran.

The crisis in Venezuela

Venezuela has been gripped by a simmering conflict for months, after an opposition leader declared himself interim president and urged the military to back his claim. The current president, Nicolás Maduro, has refused to step down, dividing the international community between the government and the opposition.

Washington has recognized Juan Guaidó, the head of the country’s legislature and the leader of the opposition, as Venezuela’s rightful interim president, putting the United States directly at odds with Russia. Mr. Pompeo and Mr. Lavrov discussed Venezuela, among other issues, on the sidelines of an Arctic Council meeting in Finland earlier this month.

“We want the Cubans out, we want the Iranians out, Russia’s military out,” Mr. Pompeo told reporters in Finland. “We started to talk about how our interests might be able to find a way forward. I don’t know that we’ll get to the right place, but we’ll have further conversations.”